Group #18016217 — subgroups

Subgroups — C₁₉×#10258 #18016217

Order 4864.

526 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3077	C₂	1	2	yes	maximal
3	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1493	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#533	C₂²	1	2	yes	—
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#478	—	2	4	no	—
9	C₁₉×#477	—	2	2	no	—
10	C₁₉×#476	—	2	2	no	—
11	C₁₉×#474	—	2	2	no	—
12	C₁₉×#467	—	2	2	no	—
13	C₁₉×#462	—	2	2	no	—
14	C₁₉×#428	—	2	2	no	—
15	C₁₉×#423	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#418	—	2	2	no	—
18	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×Q₈⋊C₈	—	2	4	no	—
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂×Q₁₆×C₁₉	—	2	2	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₁₉×#125	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₁₉×C₂²⋊Q₈	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₁₉×#117	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#107	—	2	4	no	—
41	C₁₉×#107	—	2	2	no	—
42	C₁₉×#106	—	2	4	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×C₄⋊C₈	—	2	2	no	—
45	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
46	C₁₉×#103	—	2	4	no	—
47	C₁₉×#102	—	2	4	no	—
48	C₁₉×#102	—	2	4	no	—
49	C₁₉×C₂²⋊C₈	—	4	4	no	—
50	C₄×C₈×C₁₉	—	2	2	no	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	Q₁₆	1	2	yes	complemented
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	Q₁₆×C₁₉	—	8	2	no	—
67	M₁₆×C₁₉	—	4	2	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	4	no	—
72	C₂×C₈×C₁₉	—	4	1	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₂×C₈×C₁₉	—	4	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	4	2	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₂²⋊C₄×C₁₉	—	4	2	no	—
83	C₂²⋊C₄×C₁₉	—	4	2	no	—
84	C₄²×C₁₉	—	4	2	no	—
85	C₄²×C₁₉	C₂×D₄	1	2	yes	—
86	C₄²×C₁₉	C₂×D₄	1	2	yes	—
87	#10258	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	—	4	2	no	—
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	—	4	1	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	#121	1	1	yes	characteristic
94	Q₈×C₁₉	—	4	4	no	—
95	Q₈×C₁₉	—	4	2	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	D₄×C₁₉	—	2	4	no	—
98	D₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	—	8	1	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	#120	1	2	yes	—
110	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#121	1	2	yes	—
112	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#137	1	2	yes	—
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	—	4	4	no	—
118	C₈×C₁₉	—	4	2	no	—
119	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
120	#3077	C₂×C₁₉	1	2	yes	—
121	#1954	C₂×C₁₉	1	1	yes	characteristic
122	#1493	C₂×C₁₉	1	2	yes	complemented
123	#1292	C₂×C₁₉	1	1	yes	characteristic, complemented
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	4	4	no	—
127	C₂²×C₁₉	—	4	2	no	—
128	C₂²×C₁₉	—	8	2	no	—
129	C₂²×C₁₉	—	8	1	no	—
130	C₂²×C₁₉	—	8	1	no	—
131	C₂²×C₁₉	#392	1	1	yes	characteristic
132	C₂²×C₁₉	#467	1	1	yes	characteristic
133	C₂²×C₁₉	#470	1	1	yes	characteristic
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	8	1	no	—
137	C₄×C₁₉	—	8	2	no	—
138	C₄×C₁₉	—	8	2	no	—
139	C₄×C₁₉	#451	1	2	yes	—
140	C₄×C₁₉	#452	1	2	yes	—
141	C₄×C₁₉	#453	1	1	yes	characteristic
142	C₄×C₁₉	#454	1	1	yes	characteristic
143	#533	C₂²×C₁₉	1	2	yes	—
144	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
145	#478	—	2	4	no	—
146	#477	—	2	2	no	—
147	#476	—	2	2	no	—
148	#474	—	2	2	no	—
149	#467	—	2	2	no	—
150	#462	—	2	2	no	—
151	#428	—	2	2	no	—
152	#423	C₂²×C₁₉	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
154	#418	—	2	2	no	—
155	C₂×C₂²⋊C₈	—	2	2	no	—
156	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
157	Q₈⋊C₈	—	2	4	no	—
158	C₂×C₁₉	—	2	1	no	—
159	C₂×C₁₉	—	2	1	no	—
160	C₂×C₁₉	—	8	2	no	—
161	C₂×C₁₉	#2001	1	1	yes	characteristic
162	C₂×C₁₉	#2006	1	1	yes	characteristic
163	C₂×C₁₉	#2017	1	1	yes	characteristic
164	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
165	C₂³×C₄	—	2	1	no	—
166	C₂×Q₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂²×C₈	—	2	1	no	—
169	C₂²×C₈	D₄×C₁₉	1	2	yes	—
170	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
171	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
172	#125	—	2	2	no	—
173	C₂²⋊Q₈	—	2	2	no	—
174	C₂²⋊Q₈	—	2	2	no	—
175	C₄×Q₈	—	2	2	no	—
176	C₄×Q₈	—	2	2	no	—
177	C₄×D₄	—	2	2	no	—
178	C₄×D₄	—	2	2	no	—
179	#117	—	2	2	no	—
180	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
181	C₂×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
183	#107	—	2	4	no	—
184	#107	—	2	2	no	—
185	#106	—	2	4	no	—
186	C₄⋊C₈	—	2	2	no	—
187	C₄⋊C₈	—	2	2	no	—
188	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
189	#103	—	2	4	no	—
190	#102	—	2	4	no	—
191	#102	—	2	4	no	—
192	C₂²⋊C₈	—	4	4	no	—
193	C₄×C₈	—	2	2	no	—
194	C₁₉	#10258	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁴	—	2	1	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	2	2	no	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	—	2	1	no	—
200	C₂×D₄	—	2	2	no	—
201	C₂×D₄	Q₁₆×C₁₉	1	2	yes	complemented
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	4	2	no	—
204	C₂²×C₄	—	4	2	no	—
205	C₂²×C₄	—	4	1	no	—
206	C₂²×C₄	—	4	1	no	—
207	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
209	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
210	Q₁₆	—	8	2	no	—
211	M₁₆	—	4	2	no	—
212	M₁₆	—	4	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	4	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	—	4	2	no	—
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	2	2	no	—
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	4	2	no	—
225	C₄⋊C₄	—	4	2	no	—
226	C₂²⋊C₄	—	4	2	no	—
227	C₂²⋊C₄	—	4	2	no	—
228	C₄²	—	4	2	no	—
229	C₄²	C₂×D₄×C₁₉	1	2	yes	—
230	C₄²	C₂×D₄×C₁₉	1	2	yes	—
231	C₂³	—	2	2	no	—
232	C₂³	—	4	2	no	—
233	C₂³	—	4	2	no	—
234	C₂³	—	4	1	no	—
235	C₂³	—	4	1	no	—
236	C₂³	C₁₉×#121	1	1	yes	characteristic
237	Q₈	—	4	4	no	—
238	Q₈	—	4	2	no	—
239	Q₈	—	4	2	no	—
240	D₄	—	2	4	no	—
241	D₄	—	4	2	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	8	2	no	—
250	C₂×C₄	—	8	1	no	—
251	C₂×C₄	—	8	1	no	—
252	C₂×C₄	C₁₉×#120	1	2	yes	—
253	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
254	C₂×C₄	C₁₉×#121	1	2	yes	—
255	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
256	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
257	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
258	C₂×C₄	C₁₉×#137	1	2	yes	—
259	C₈	—	4	2	no	—
260	C₈	—	4	4	no	—
261	C₈	—	4	2	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	—	4	4	no	—
265	C₂²	—	4	2	no	—
266	C₂²	—	8	2	no	—
267	C₂²	—	8	1	no	—
268	C₂²	—	8	1	no	—
269	C₂²	C₁₉×#392	1	1	yes	characteristic
270	C₂²	C₁₉×#467	1	1	yes	characteristic
271	C₂²	C₁₉×#470	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	2	no	—
274	C₄	—	8	1	no	—
275	C₄	—	8	2	no	—
276	C₄	—	8	2	no	—
277	C₄	C₁₉×#451	1	2	yes	—
278	C₄	C₁₉×#452	1	2	yes	—
279	C₄	C₁₉×#453	1	1	yes	characteristic
280	C₄	C₁₉×#454	1	1	yes	characteristic
281	C₂	—	2	1	no	—
282	C₂	—	2	1	no	—
283	C₂	—	8	2	no	—
284	C₂	C₁₉×#2001	1	1	yes	characteristic
285	C₂	C₁₉×#2006	1	1	yes	characteristic
286	C₂	C₁₉×#2017	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3249

C₂

yes

maximal, characteristic, complemented

C₁₉×#3077

C₂

yes

maximal

C₁₉×#1954

C₂

yes

maximal, characteristic

C₁₉×#1493

C₂

yes

maximal, complemented

C₁₉×#1292

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂²

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#478

—

C₁₉×#477

—

C₁₉×#476

—

C₁₉×#474

—

C₁₉×#467

—

C₁₉×#462

—

C₁₉×#428

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#418

—

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×Q₈⋊C₈

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#103

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₁₆

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#10258

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

#120

yes

—

110

C₂×C₄×C₁₉

#120

yes

characteristic

111

C₂×C₄×C₁₉

#121

yes

—

112

C₂×C₄×C₁₉

#127

yes

characteristic

113

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

114

C₂×C₄×C₁₉

#135

yes

characteristic

115

C₂×C₄×C₁₉

#137

yes

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₈×C₁₉

—

119

#3249

C₂×C₁₉

yes

characteristic, complemented

120

#3077

C₂×C₁₉

yes

—

121

#1954

C₂×C₁₉

yes

characteristic

122

#1493

C₂×C₁₉

yes

complemented

123

#1292

C₂×C₁₉

yes

characteristic, complemented

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

#392

yes

characteristic

132

C₂²×C₁₉

#467

yes

characteristic

133

C₂²×C₁₉

#470

yes

characteristic

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

#451

yes

—

140

C₄×C₁₉

#452

yes

—

141

C₄×C₁₉

#453

yes

characteristic

142

C₄×C₁₉

#454

yes

characteristic

143

#533

C₂²×C₁₉

yes

—

144

C₂×C₄×D₄

C₂²×C₁₉

yes

characteristic

145

#478

—

146

#477

—

147

#476

—

148

#474

—

149

#467

—

150

#462

—

151

#428

—

152

#423

C₂²×C₁₉

yes

—

153

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

154

#418

—

155

C₂×C₂²⋊C₈

—

156

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

157

Q₈⋊C₈

—

158

C₂×C₁₉

—

159

C₂×C₁₉

—

160

C₂×C₁₉

—

161

C₂×C₁₉

#2001

yes

characteristic

162

C₂×C₁₉

#2006

yes

characteristic

163

C₂×C₁₉

#2017

yes

characteristic

164

C₂²×D₄

D₄×C₁₉

yes

characteristic

165

C₂³×C₄

—

166

C₂×Q₁₆

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₂²×C₈

D₄×C₁₉

yes

—

170

C₄⋊Q₈

D₄×C₁₉

yes

—

171

C₄⋊Q₈

D₄×C₁₉

yes

—

172

#125

—

173

C₂²⋊Q₈

—

174

C₂²⋊Q₈

—

175

C₄×Q₈

—

176

C₄×Q₈

—

177

C₄×D₄

—

178

C₄×D₄

—

179

#117

—

180

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

181

C₂×C₂²⋊C₄

—

182

C₂×C₄²

C₂³×C₁₉

yes

characteristic

183

#107

—

184

#107

—

185

#106

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

D₄×C₁₉

yes

—

189

#103

—

190

#102

—

191

#102

—

192

C₂²⋊C₈

—

193

C₄×C₈

—

194

C₁₉

#10258

yes

characteristic, direct product factor, Sylow

195

C₂⁴

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

Q₁₆×C₁₉

yes

complemented

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

208

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

209

C₂²×C₄

#41×C₁₉

yes

characteristic

210

Q₁₆

—

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₂²⋊C₄

—

227

C₂²⋊C₄

—

228

C₄²

—

229

C₄²

C₂×D₄×C₁₉

yes

—

230

C₄²

C₂×D₄×C₁₉

yes

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

C₁₉×#121

yes

characteristic

237

Q₈

—

238

Q₈

—

239

Q₈

—

240

D₄

—

241

D₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

C₁₉×#120

yes

—

253

C₂×C₄

C₁₉×#120

yes

characteristic

254

C₂×C₄

C₁₉×#121

yes

—

255

C₂×C₄

C₁₉×#127

yes

characteristic

256

C₂×C₄

C₂×Q₁₆×C₁₉

yes

characteristic

257

C₂×C₄

C₁₉×#135

yes

characteristic

258

C₂×C₄

C₁₉×#137

yes

—

259

C₈

—

260

C₈

—

261

C₈

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

C₁₉×#392

yes

characteristic

270

C₂²

C₁₉×#467

yes

characteristic

271

C₂²

C₁₉×#470

yes

characteristic

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

C₁₉×#451

yes

—

278

C₄

C₁₉×#452

yes

—

279

C₄

C₁₉×#453

yes

characteristic

280

C₄

C₁₉×#454

yes

characteristic

281

C₂

—

282

C₂

—

283

C₂

—

284

C₂

C₁₉×#2001

yes

characteristic

285

C₂

C₁₉×#2006

yes

characteristic

286

C₂

C₁₉×#2017

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂²×D₄×C₁₉

D₄

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#3249	C₂	semidirect
4. C₁₉×#1493	C₂	semidirect
5. C₁₉×#1292	C₂	semidirect
57. C₂×D₄×C₁₉	Q₁₆	semidirect
87. #10258	C₁₉	direct (N × H)
119. #3249	C₂×C₁₉	semidirect
122. #1493	C₂×C₁₉	semidirect
123. #1292	C₂×C₁₉	semidirect
194. C₁₉	#10258	direct (N × H)
201. C₂×D₄	Q₁₆×C₁₉	semidirect

H ≅ G/N

type

1. C₁₉×#3249

C₂

semidirect

4. C₁₉×#1493

C₂

semidirect

5. C₁₉×#1292

C₂

semidirect

57. C₂×D₄×C₁₉

Q₁₆

semidirect

87. #10258

C₁₉

direct (N × H)

119. #3249

C₂×C₁₉

semidirect

122. #1493

C₂×C₁₉

semidirect

123. #1292

C₂×C₁₉

semidirect

194. C₁₉

#10258

direct (N × H)

201. C₂×D₄

Q₁₆×C₁₉

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3249	2
C₁₉×#3077	2
C₁₉×#1954	2
C₁₉×#1493	2
C₁₉×#1292	2
#10258	19

subgroup

index

C₁₉×#3249

C₁₉×#3077

C₁₉×#1954

C₁₉×#1493

C₁₉×#1292

#10258

Subgroups — C₁₉×#10258 #18016217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10258 #18016217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10258 #18016217